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Present Value with Constant Perpetual Growth Rate

Present Value with Constant Perpetual Growth Rate

Present value with constant perpetual growth rate is often applied to find present value or current price of ordinary share (common stock).

Time Line

Which

  • C0 : base amount at the beginning of period 1 (Period 0) for constant perpetual growth rate
  • g: constant perpetual growth rate

Question

The XYZ  Co. has just paid a cash dividend of $2 per share. Potential investors require a 16 percent return from investments. If the dividend is expected to grow at a steady 8 percent per year, what is the current value of the stock? What will the stock be worth in five years?

Solution

  • The current value of the stock

          Do=$2

Po=D1/(r-g)=[D0*(1+g)]/(r-g)

=[2*(1+0.08)]/(0.16-0.08)=$27

So current price =$27

  • Stock price at the next five years

          Dividend in five year

=> D5 =Do*(1+g)5 =$2*(1+0.08)5 =$2.9387, so price of stock in five years:

=>P5 = D5 *(1+g)/(r-g)

= $2.9387 *(1+0.08)/(0.16-0.08)=$39.67 or

        P= Po*(1+g)5 =$27 *(1+0.08)5 =$39.67

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